Finding Lanch Angle (without initial velocity)

[peterbishop]

Homework Statement

Exact question: A hobby rocket reaches a height of 35m and lands 259m from the launch point. What was the angle of launch?

We know...
Xmax = 259m
Ymax = 35m
Xo and Xmax are at equal y values, or heights, 0 in my chosen coordinate system

Homework Equations

1) Xmax = (Vo^2 * sin(2 * theta))/g
2) Ymax = (Vo * sin(theta))^2 / g
3) Vy at max height is zero
4) time of Xmax = (2Vo * sin(theta)) / g
5) time of Ymax = (Vo * sin(theta)) / g
6) Y = Yo + Vosin(theta)t - (1/2)gt^2
7) X = Xo + Vocos(theta)t
8) Vfy^2 - Voy^2 = -2gh (or something like that, I haven't used this equation in conjunction with projectile motion before)

The Attempt at a Solution

This problem has stumped me for a long time. I remember I had something like it in high school as well that I had a hard time with. It would take up way too much room to type out all my wrong solutions, but I'll go over some of the stuff I've tried today. I tried using equations 1 and 2, setting them equal to their respective known values. I tried to solve for Vo in the Ymax equation, getting Vo = 26.2/sin(theta). I tried plugging that into the Xmax equasion, getting a messy kind of simplified 3.7 = sin(2*theta)/(sin^2(theta)). I wasn't sure what to do with that then, trig is not my strong point and there has to be a better way to do this problem. I've tried using equations 6 and 7, solving for time in 7 and plugging it back into 6 but that didn't work either. Any advice on how to go about solving this problem and ones like it would be helpful, I'm sure it's just something I'm overlooking or a substitution I haven't thought about.

 

[ehild]

Your second equation is wrong: The correct one is Ymax = (Vo * sin(theta))^2 /(2g).

(The vertical motion of the projectile is described with the equations (6) and v_y = vo sin(theta)-gt.
As you know correctly, v_y=0 at maximum height, the time to reach it is t = vo sin(theta)/g. Substitute for t in eq. 6, you get y(max)=(vo sin(theta))^2/(2g) )

Knowing y(max), you get vo sin(theta). The first equation yields vo^2 * sin(2 * theta). You know the trigonometric eq.
sin(2* theta)=2 sin (theta)*cos(theta).

You have two equations for vo and theta. Cancel vo, solve for theta, then get vo.

ehild

 

[JaredJames]

https://www.physicsforums.com/showthread.php?t=434921

I'm going to point you here as well, I just answered this and it's a similar question. The only difference is you'd have to resolve for the ascent time as well.

If you can understand what I've done there, you can work out how to solve your question.

Jared

 

[rl.bhat]

Homework Statement

Exact question: A hobby rocket reaches a height of 35m and lands 259m from the launch point. What was the angle of launch?

We know...
Xmax = 259m
Ymax = 35m
Xo and Xmax are at equal y values, or heights, 0 in my chosen coordinate system

Since you want only the angle of launch, find the expressions for Ymax and Xmax.
If t is he time to reach Ymax, 2t will be the time to reach Xmax.

2vo^2*sinθ*cosθ = Xmax ...(1)
vo^2*sin^2(θ) = 2*g*Ymax ...(2)

Divide (2) by (1) and solve for θ.

 

[rwisz]

It seems like you have made some progress in approaching this problem, but there are a few things you could try to find the launch angle without initial velocity. First, you could try using the range equation (X = V^2 * sin(2*theta) / g) and solving for theta. This would involve substituting in the known values for range and acceleration due to gravity, and then solving for theta. Another approach could be to use the time of flight equation (t = 2 * Vo * sin(theta) / g) and solving for theta, again by substituting in the known values. Additionally, you could try graphing the equations in terms of theta and looking for the intersection point where both equations (range and time of flight) are satisfied. This could give you a more visual understanding of the problem and help you find the launch angle. Keep in mind that you may need to use trial and error to find a solution that satisfies both equations. Good luck!